Parity violation and the mean field approximation for the anyon gas

TL;DR

This paper investigates the validity of the mean field approximation for the anyon gas by analyzing scattering processes and parity violation, proposing a criterion based on the average scattering angle and interaction effects.

Contribution

It introduces a novel approach linking parity violation and scattering to justify the mean field approximation for anyons, emphasizing the role of non-conventional interactions.

Findings

Parity violation leads to a nonzero average scattering angle.

The mean field approximation is valid when the mean radius exceeds interparticle separation.

A specific interaction is crucial for the approximation's validity.

Abstract

We examine an approach to justifying the mean field approximation for the anyon gas, using the scattering of anyons. Parity violation permits a nonzero average scattering angle, from which one can extract a mean radius of curvature for anyons. If this is larger than the interparticle separation, one expects that the graininess of the statistical magnetic field is unimportant, and that the mean field approximation is good. We argue that a non-conventional interaction between anyons is crucial, in which case the criterion for validity of the approximation is identical to the one deduced using a self-consistency argument.